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We investigate in this paper the simultaneous effects of electric field, couple stress, porous parameter and slip at the permeable surface on the generalized dispersion of an unsteady convective diffusion in a poorly conducting fluid in a channel bounded by porous layers. A two dimensional flow has been considered and the resulting partial differential equations have been solved analytically. The solutions are computed and the results show that the solute is dispersed relative to a plane moving with the mean speed of couple stress poorly conducting fluid with a relative unsteady dispersion coefficient. These relative unsteady dispersion coefficients are numerically computed and found that they increase with the increase in porous parameter and decrease with an increase in couple stress parameters. We have also estimated the contribution of diffusion and pure convection on the generalized dispersion coefficient. The effect of pure convection, neglecting diffusion terms on mean concentration is computed and the results show that the effect of pure convection decreases mean concentration compared to combined effect of convection and diffusion.

The purpose of this paper is to re-examine the assumptions implicit in Leveque’s approximation, and the variation of the temperature and the thickness of the boundary layer were illustrated using the developed solution. The analytical solutions are then checked against numerical solution programming by FORTRAN code obtained via using Runge–Kutta fourth-order (RK4) method. Finally, other important thermal results obtained from this analysis, such as approximate Nusselt number in the thermal entrance region, was discussed in detail. After that, the analytical results of the present paper are validated with certain previous investigations which were found in the specialized literature.

By defining a similarity variable, the governing equations are reduced to a dimensionless equation with an analytic solution in the entrance region. This paper gives justification for the similarity variable via scaling analysis, details the process of converting to a similarity form and presents a similarity solution. The calculation methodology for numerical resolution is based on the RK4 technique.

The profiles of the solutions are provided from which the authors infer that the numerical and exact solutions agreed very well. Another result that the authors obtained from this paper is the number of Nusselt in the thermal entrance region for which a parametric study was carried out and discussed well for the impact of scientific contribution.

The novelty of this paper is the application of the RK4 with a step size control, as a sequential numerical method of a ODEs system compared with the exact similarity solution of the thermal boundary layer problem.

The model, presented here, is developed to study the axial dispersion and distribution of oil particle concentration in the presence of coriolis force of oil spilled under solid ice cover. The movement of oil slick is obtained by employing perturbation technique and the dispersion of oil is studied using generalized dispersion model proposed by Gill (1967). The mean concentration is computed by introducing a slug of finite length separated from pure solvent using suitable impermeable barriers by varying the dimensionless time, axial distance and length of solute slug. The results obtained are discussed in detail with the help of graphs and tables.

The flow development and heat transfer in a differentially heated cavity containing a non‐Newtonian fluid is studied using CFD techniques. Investigations are made for a fluid obeying a power‐law type behaviour, for a nominal Rayleigh number of 10⁵. Both dilatant and pseudoplastic regimes are considered and the Nusselt number is obtained for a range of power‐law index values. The results, given in a graphical and tabular form, suggest that deviations from Newtonian stress‐strain behaviour can lead to large changes in overall heat transfer. These changes are due to the behaviour of the wall boundary layers. In the dilatant, or shear‐thickening regime, the isothermal wall layers are thick and slow‐moving; as a consequence, buoyancy induced flow affects the whole of the cavity volume. In contrast, the pseudoplastic (or shear‐thinning) regime leads to thin, fast‐moving wall layers whose effect does not propagate to the core of the cavity which remains stagnant. This behaviour, which is directly attributable to the local value of the fluid viscosity, causes the average Nusselt number to decrease with the power‐law index, n. Pseudoplastic fluids are therefore better at conducting heat than Newtonian fluids, and conversely dilatant fluids are worse. The information contained in this paper is of general interest to workers in heat transfer, but is more specifically relevant to researchers in non‐Newtonian fluids. Example applications include biotechnology, where close temperature control of bio‐cultures in enclosed vessels is required, the food processing industry, the metals casting industry and areas where heat transfer in fine suspensions is required.

In many industrial applications of magnetic fluid dynamics it is important to control the motion of the surface of liquids. In aluminium electrolysis cells, large surface deformations of the molten aluminium are undesired, and it would be useful to have the possibility to recognize the surface deviation. This includes the problem of reconstructing a free boundary between the conducting fluids. We have investigated how the interface between two fluids of different conductivity assumed in a highly simplified model of an aluminium electrolysis cell could be reconstructed by means of external magnetic field measurements. Forward simulations of the magnetic field generated by the impressed current are done by applying the FEM software code FEMLAB. Several interface shapes which can be realized in experiments are investigated and a strategy for identifying the main interface characteristics using magnetic field measurements as an initial guess to the solution of the inverse problem is proposed.

A numerical study has been conducted for natural convection heat transfer for air around two vertically separated horizontal heated cylinders placed inside an isothermal rectangular enclosure having finite wall conductances. The interaction between convection in the fluid filled cavity and conduction in the walls surrounding the cavity is investigated. Results have been obtained for Rayleigh numbers (Ra) between 10³ and 10⁶, dimensionless wall thickness (W) between 0.5 and 1.375 and dimensionless wall‐fluid thermal conductivity ratio (α) between 0.01 and 5.0. The results indicate that wall heat conduction reduces the average temperature differences across the cavity, partially stabilizes the flow, and decreases natural convection heat transfer. The overall heat transfer coefficient for both cylinders is correlated with CRaⁿ for different W and α.

Hydrothermal waves represent the preferred mode of instability of the so-called Marangoni flow for a wide range of liquids and conditions. The related features in classical rectangular containers have attracted much attention over recent years owing to the relevance of these oscillatory modes to several techniques used for the production of single crystals of semiconductor or oxide materials. Control or a proper knowledge of convective instabilities in these systems is an essential topic from a material/product properties saving standpoint. The purpose of this study is to improve our understanding of these phenomena in less ordinary circumstances.

This short paper reports on a numerical model developed to inquire specifically about the role played by sudden changes in the available cross-section of the shallow cavity hosting the liquid. Although accounting for the spanwise dimension would be necessary to derive quantitative results, the approach is based on the assumption of two-dimensional flow, which, for high-Pr fluids, is believed to retain the essence of the involved physical processes.

Results are presented for the case of a fluid with Pr = 15 filling an open container with a single backward-facing or forward-facing step on the bottom wall or with an obstruction located in the centre. It is shown that the presence of steps in the considered geometry can lead to a variety of situations with significant changes in the local spectral content of the flow and even flow stabilization in certain circumstances. The role of thermal boundary conditions is assessed by considering separately adiabatic and conducting conditions for the bottom wall.

Although a plethora of studies have been appearing over recent years motivated, completely or in part, by a quest to identify new means to mitigate these instabilities and produce accordingly single crystals of higher quality for the industry, unfortunately, most of these research works were focusing on very simple geometries. In the present paper, the causality and interdependence among all the kinematic and thermal effects mentioned above is discussed.

The current investigation is communicated to analyze the characteristics of squeezed second grade nanofluid flow enclosed by infinite channel in the existence of both heat generation and variable viscosity. The leading non-linear energy and momentum PDEs are converted into non-linear ODEs by using suitable analogous approach.

Then the acquired non-linear problem is numerically calculated by using Bvp4c (built in) technique in MATLAB.

The influence of certain appropriate physical parameters, namely, squeezed number, fluid parameter, Brownian motion, heat generation, thermophoresis parameter, Prandtl number, Schmidt number and variable viscosity parameter on temperature, velocity and concentration distributions are studied and deliberated in detail. Numerical calculations of Sherwood number, Nusselt number and skin friction for distinct estimations of appearing parameters are analyzed through graphs and tables. It is examined that for large values of squeezing parameter, the velocity profile increases, whereas opposite behavior is noticed for large values of variable viscosity and fluid parameter. Moreover, temperature profile increases for large values of Brownian motion, thermophoresis parameter and squeezed parameter and decreases by increases Prandtl number and heat generation. Moreover, concentration profile increases for large values of Brownian motion parameter and decreases by increases thermophoresis parameter, squeezed parameter and Schmidt number.

No one has ever taken infinite squeezed channel having second grade fluid model with variable viscosity and heat generation.

Thermally driven flow in a tall inclined cavity bounded by porous layers is studied analytically and numerically. A constant heat flux is applied for heating and cooling of two opposing walls of the cavity, while the other two are insulated. The Beavers—Joseph slip condition on velocity is applied at the interface between the fluid and porous layers. An analytical solution is obtained by assuming parallel flow in the core region of the cavity and a numerical solution by solving the complete governing equations. The flow and heat transfer variables are obtained in terms of the Rayleigh number, Ra, slip condition parameter N and angle of inclination of the cavity Φ. The critical Rayleigh numbers for the onset of convection in a layer heated from below are predicted for various hydrodynamic boundary conditions. The results for a fluid layer bounded by solid walls (N → ∞) and by free surfaces (N → 0) emerge from the present analysis as limiting cases.